Question

Three pumps working 8 hours a day can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Answer 1

Hint: Find the work done by 3 pumps in 1 hour. Thus find work done by 1 pump in 1 hour. Now find work done by 4 pumps in 1 hour. Thus we will get work done by 4 pumps in a day.

Complete step-by-step answer:
It is said that 3 pumps work 8 hours a day.
These 3 pumps can empty a tank in 2 days.
8 hours a day means these 3 pumps work \[\left( 2\times 8 \right)\] hours in 2 days, which means that they can empty a tank in 16 hours.
Now let us find the work done by these tanks in one hour.
They work 16 hours to empty a particular tank.
\[\therefore \]Work done by 3 pumps in one hour = \[{}^{1}/{}_{16}\].
\[{}^{1}/{}_{16}\] is the work done by 3 pumps. Now let us find the work done by one single pump in 1 hour.
Work done by 1 pump in 1 hour = \[\dfrac{1}{3\times 16}=\dfrac{1}{48}\].
Now we need to find the work done by 4 pumps.
\[\therefore \] Work done by 4 pumps = \[4\times \] work done by 1 pump = \[4\times \dfrac{1}{48}=\dfrac{1}{12}\].
Thus \[\dfrac{1}{12}\] is the work done by 4 pumps in 1 hour.
Thus the 4 pumps together take 12 hours to empty the tank in 1 day.
Hence, the whole tank is emptied by 4 pumps in 12 hours a day.

Note:Don’t leave the answer as \[\dfrac{1}{12}\], because it is the work done by the 4 pumps in 1 hour. What we need is the total hours the pump worked in a single day to drain the tank, which will be 12 hours. Thus remember this point, if it was to find the work done in 1 hour, we can leave it as such.